Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 592 · 40 sums

The method (Split into easy parts): (a + b)² = a² + 2ab + b². (a − b)² = a² − 2ab + b². (a + b)(a − b) = a² − b²; so a² − b² = (a + b)(a − b). a² + b² = (a + b)² − 2ab = (a − b)² + 2ab.

1. 1.Use a² − b² = (a + b)(a − b) to find 75² − 32².
2. 2.Use (a − b)² = a² − 2ab + b² to find 18².
3. 3.Use (a + b)(a − b) = a² − b² to find 106 × 94.
4. 4.Find the value of x² + 2xy + y² when x = 11 and y = 4.
5. 5.Use (a + b)² = a² + 2ab + b² to find 39².
6. 6.Use (a + b)² = a² + 2ab + b² to find 32².
7. 7.Use (a − b)² = a² − 2ab + b² to find 96².
8. 8.Use (a − b)² = a² − 2ab + b² to find 35².
9. 9.Use (a − b)² = a² − 2ab + b² to find 89².
10. 10.Use (a + b)² = a² + 2ab + b² to find 64².
11. 11.Use (a + b)(a − b) = a² − b² to find 81 × 79.
12. 12.Use (a + b)(a − b) = a² − b² to find 25 × 15.
13. 13.Use (a + b)² = a² + 2ab + b² to find 63².
14. 14.If a − b = 3 and ab = 18, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 64².
16. 16.Use (a + b)² = a² + 2ab + b² to find 78².
17. 17.Find the value of x² + 2xy + y² when x = 7 and y = 1.
18. 18.If a − b = 10 and ab = 11, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 48² − 31².
20. 20.Find the value of x² − y² when x = 5 and y = 4.
21. 21.Use (a + b)² = a² + 2ab + b² to find 25².
22. 22.If a + b = 10 and ab = 9, what is a² + b²?
23. 23.Use (a + b)² = a² + 2ab + b² to find 95².
24. 24.Use (a + b)(a − b) = a² − b² to find 23 × 17.
25. 25.Find the value of x² − 2xy + y² when x = 4 and y = 3.
26. 26.Use (a − b)² = a² − 2ab + b² to find 62².
27. 27.Use (a − b)² = a² − 2ab + b² to find 95².
28. 28.Find the value of x² + 2xy + y² when x = 14 and y = 1.
29. 29.Find the value of x² − y² when x = 5 and y = 1.
30. 30.Use (a − b)² = a² − 2ab + b² to find 38².
31. 31.Use (a − b)² = a² − 2ab + b² to find 12².
32. 32.Find the value of x² − 2xy + y² when x = 15 and y = 3.
33. 33.Use a² − b² = (a + b)(a − b) to find 92² − 31².
34. 34.Use a² − b² = (a + b)(a − b) to find 68² − 39².
35. 35.If a − b = 5 and ab = 6, what is a² + b²?
36. 36.If a − b = 2 and ab = 3, what is a² + b²?
37. 37.Find the value of x² − y² when x = 3 and y = 1.
38. 38.Use (a − b)² = a² − 2ab + b² to find 69².
39. 39.If a + b = 4 and ab = 3, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 30² − 15².

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